Looking at the minimum distinct character challenges linked it does seem like while there are a couple it's not a very well liked scoring criterion on it's own.
"Do X but with minimum characters" is just not interesting on it's own anymore. Unlike other scoring criteria most challenges with this criterion end up feeling pretty much the same.
Of course restricted-source or other special rules could turn this on its head. I just don't think we should anticipate a whole lot more of these challenges.
I still think that in the end the scant challenges we have may be worth tagging, but I think we can find a more useful tag by broadening the scope of this tag.
I suggest we add a single tag which just indicates that the scoring for the challenge involves the distinct characters rather than just all the characters.
So distinct-scoring + code-golf would be minimum number of distinct characters, and distinct-scoring + code-bowling would be the maximum number of distinct characters.
This widens the potential pool on the tag a bit to include more challenges which really are very similar. It's also more open to variation which I think this type of challenge is in desperate need of if it is going to keep being asked.